• 论文
主办单位:煤炭科学研究总院有限公司、中国煤炭学会学术期刊工作委员会
基于分形表征的粗糙微纳米孔隙瓦斯气体传输方程
  • Title

    Gas transport equation based on fractal characterization of rough micro-nano pores

  • 作者

    王登科李文睿魏建平于充张凯旋

  • Author

    WANG Dengke1,2,3,4 ,LI Wenrui1,3 ,WEI Jianping1,3,4 ,YU Chong1,3 ,ZHANG Kaixuan1,3

  • 单位

    河南理工大学 河南省瓦斯地质与瓦斯治理重点实验室-省部共建国家重点实验室培育基地中国矿业大学 深部岩土力学与地下工程国家重点实验室河南理工大学 安全科学与工程学院煤炭安全生产河南省协同创新中心

  • Organization
    1. State Key Laboratory Cultivation Base for Gas Geology and Gas Control,Henan Polytechnic University,Jiaozuo  454000,China; 2. State Key Laboratory for GeoMechanics and Deep Underground Engineering,China University of Mining & Technology,Xuzhou  221116,China; 3. School of Safety Science and Engi-neering,Henan Polytechnic University,Jiaozuo  454000,China; 4. The Collaborative Innovation Center of Coal Safety Production of Henan,Jiaozuo  454000, China
  • 摘要

    为揭示煤体孔隙内表面粗糙微结构对瓦斯传输的影响机制,准确研究粗糙孔隙中的瓦斯气体传输规律,运用自相似特性分形理论推导出了微纳米孔隙内壁面粗糙元有效平均高度和孔隙有效半径的精确数学表达式;采用Optical Tensiometer设备对取自煤体孔隙内壁表面进行3D形貌结构量化分析,将所得关键参数代入相对粗糙度表达式求得对应值为0.352;结合流体速度滑移效应和分子扩散传输机理,推导出了粗糙微纳米孔隙中的瓦斯气体滑流修正传输方程和非连续流扩散传输方程,再通过等效转换原则推导出微纳米孔隙内的视渗透率模型;考虑到煤体纳米级孔隙难以进行精确测量表征和规避孔隙连通性对气体传输的影响,选取结构规整的纳米级圆孔阳极氧化铝薄膜作为气体流动通道载体;基于气体压差穿透实验原理,利用实验室PMI微渗透率设备进行了纳米级孔隙薄膜的渗透性实验,将实验结果所测得的渗透率数据与本文理论模型计算值进行了对比分析。研究结果表明:基于分形表征建立的粗糙微纳米孔隙瓦斯气体传输方程合理可靠,考虑孔隙粗糙度对瓦斯流动的影响是应该且必须的,以分形理论表征的孔隙相对粗糙度公式比前人所提出的孔隙粗糙度经验性公式更为精确,研究结果可为在分形拓扑领域中构建自仿射粗糙微通道的气体流动模拟研究工作中提供借鉴。

  • Abstract
    In order to reveal the effect mechanism of rough microstructures of the inner surface of coal pores on gas transport and accurately study the law of gas transport in rough pores,the precise mathematical expressions of effective average height and effective radius of rough elements in micro-nano pore were derived based on fractal theory of self-similarity. Optical Tensiometer was used to quantitatively analyze the 3D morphology and structure of inner surface wall. The key parameters obtained from analysis were substituted into the expression of relative roughness,and the cor- responding value is 0. 352. Combining with the slip flow effect of fluid velocity and molecular diffusion transport mech- anism,the modified gas slip flow transport flux equation and molecular diffusion transport flux equation of discontinu- ous flows in rough micro-nano-pore were deduced,and then the apparent permeability model in micro-nano-pore is de- veloped in rough micro-channel by the principle of equivalent conversion. Considering that it is difficult to accurately measure and characterize the nano-pore of coal,and avoid the influence of pore connectivity on gas transport,the nano- porous anodic alumina film with regular circular holes were selected as the carrier of gas flow channel. Based on the experimental principle of gas pressure differential penetration,the permeability experiment of nano-film were carried out by using PMI micro-permeability equipment,and the permeability data measured from the experimental results were compared with the calculated values of the theoretical model in this paper. Results show that the gas transport e- quation based on fractal characterization of rough pore is reasonable and reliable. The effect of pore roughness should and must be considered in gas transport. The formula of relative roughness of pore expressed by fractal theory is more accurate than the empirical formula proposed by predecessors. In the field of fractal topology,the fractal characteriza- tion of relative roughness will provide an important theoretical support for the simulation of gas flow in self-affine rough micro-channels.
  • 关键词

    分形表征微纳米孔隙瓦斯气体相对粗糙度视渗透率模型

  • KeyWords

    fractal characterization;micro-nano pore;methane gas;relative roughness;apparent permeability model

  • 基金项目(Foundation)
    国家自然科学基金资助项目(51774118);教育部“创新团队发展计划”资助项目(IRT_16R22);深部岩土力学与地下工程国家重点实验室开放基金资助项目(SKLGDUEK1814)
  • DOI
  • Citation
    WANG Dengke,LI Wenrui,WEI Jianping,et al. Gas transport equation based on fractal characterization of rough mi- cro-nano pores[J]. Journal of China Coal Society,2019,44(11):3432-3440.
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